2016 numbers:
Lyft Revenue: $700 million
Lyft Losses: $600 million
Uber Revenue: $6 billion
Uber Losses: $2.8 billion
The ratio of revenue to losses suggest that Uber is almost twice as efficient as Lyft, and Uber's losses are probably further compounded as it includes many more future investments such as international markets that aren't yet as mature as the US market, and products/services that for which Lyft has no comparable offering like UberRush and UberEats. Lyft also doesn't have any investment in self-driving cars that I'm aware of.
This. Subsidies don't scale. When you're company does relatively few rides, you can afford to subsidize rides on the order of dollars. The more rides you do however means can only subsidize rides less and less until it has a negligible effect on a rider's decision to switch providers. At that scale, all companies will start to move away from subsidies.
Subsidies can't buy the same amount of market share at scale without losses growing linearly, which is unacceptable to investors. Subsidies will decline and should eventually disappear in mature markets even with fierce competition. Heavy subsidies really only make sense in immature markets where there is a land grab.